Fulde-ferrell Superfluidity Of 3D Three-component Fermi Gas Under SOC

The spin-orbit coupling effect associates the spin and the orbit of the particle together, providing more developments of condensed matter physics. As technology and artificial gauge potential theory advances, scientists have experimentally realized the synthetic spin-orbit coupling(SOC). Because of the interaction of SOC and the spin-selective interaction, the molecular state captures a nonzero center-of-mass momentum in such a system.We investigate the pairing physics of a three-component,spin-orbit coupled Fermi gas in the three spatial dimensions. Starting from the Hamiltonian, we obtain the single-particle dispersion under SOC and analyze the inherent asymmetry in the hyperfine state distribution. We then present the system as well as the mean-field formalism, consider different configurations of spin-dependent interactions and investigate their impact on the pairing superfluidity. There are two types of pairing states, Bardeen-Cooper-Schrieffer(BCS) state with zero center-of-mass momentum and Fulde-Ferrell(FF) state with finite center-of-mass momentum.Furthermore, judging from the minimum excitation gap, both a fully gapped FF state(gFF)and a gapless nodal FF(nFF) state exist on the diagram.